More children than Palestinian fighters are being killed in the offensive on Gaza, according to the latest United Nations statistics, despite Israel's claims to be waging a targeted military campaign.

Gaza's health ministry said that 580 Palestinians had been killed, including 155 children.

The UN's Office for the Co-ordination of Humanitarian Affairs, said that, as of Tuesday morning, 149 children had been killed, compared with 87 confirmed members of armed groups. Even including unconfirmed combatant deaths, more children would still have died.

"This is why we described the ongoing operation as a war on children," said Osama Damo, a Save the Children official in Gaza.

Dr Ashraf Al-Qidra, a health ministry spokesman, said that 84 women were also among the dead and a total of 3,650 people had been wounded.

On Tuesday, an air strike destroyed six floors of Salam Tower in the centre of Gaza City, killing at least 11 people including Ibrahim Al-Kilani, a professor of engineering, his wife and their five children. All had earlier fled from Shejaiya, where more than 70 people died in the biggest Israeli bombardment of the war on Sunday.

The impact of the conflict on children has been brought home in part by social media, which has streamed distressing photographs of small, mutilated corpses around the world. One incident, in which four boys were killed while playing football on a beach, was particularly striking, partly because journalists had been playing with them shortly beforehand and witnessed what had happened.

Human Rights Watch said in a statement that investigations of cases where there were similar casualties with no apparent military objective suggested Israel had committed war crimes.

"Israeli forces' failure to direct attacks at a military target violates the laws of war," a statement said. "Israeli forces may also have knowingly or recklessly attacked people who were clearly civilians, such as young boys, and civilian structures, including a hospital – laws-of-war violations that are indicative of war crimes."

Israel says that Hamas bears responsibility for civilian deaths because it launches rockets from and stores weapons in civilian areas.

"All civilian casualties are unintended by us, but intended by Hamas," Benjamin Netanyahu, the Israeli prime minister, said on Sunday. "They use telegenically dead Palestinians for their cause."

On Monday, the Israeli ambassador to Washington, Ron Dermer, compared the Hamas rocket attacks, responsible so far for two Israeli civilian deaths, to the Blitz and said the Israeli Defence Forces should win the Nobel Peace Prize "for fighting with unimaginable restraint".

Israel does issue warnings before some buildings are attacked. Inhabitants of a block on Omar Mukhtar Street in Gaza City received a telephone warning and all 200 were able to escape before it was destroyed at 5.30am.

Aid agencies point out that, unlike in other wars, Palestinians, enclosed by the security fence around Gaza, cannot flee. As of last night, 118,000 people were sheltering at UN schools and other facilities. But even there they may not be safe. The UN Relief and Works Agency said a girls' school housing refugees had suffered a "direct hit from Israeli shelling" yesterday. It was unclear whether any casualties had been inflicted.

On the Israeli side, 29 people have been killed, all but two soldiers.

In Cairo, attempts to negotiate a ceasefire seemed to take a step forward. Hamas and the Palestinian Authority were believed to be discussing a temporary ceasefire of five days in which talks for an easing of the joint Israeli-Egyptian blockade of Gaza could begin, though Hamas has yet to agree. It was unclear whether that would be acceptable to the Israelis. Last week they accepted an Egyptian unconditional ceasefire proposal, but have since begun a ground invasion and say that will not be stopped until it has destroyed the network of tunnels Hamas uses to infiltrate fighters into Israel.

Ban Ki-moon, the UN secretary-general, said it was his "hope and belief" that there would be an end to the fighting soon. After meeting John Kerry, the US secretary of state, in Cairo on Monday, he went to Jerusalem and the West Bank for talks with Israeli and Palestinian leaders yesterday.